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11 See in this chapter p. 155, ftnt. 3.
12 Concerning whether the output curve passes through the origin (or begins to rise
only to the right of the origin), see Knight, F. H., Risk, Uncertainty and Profit, Univer-
sity of London (Reprint), London, 1957, p. 101”ftnt.

have lower and lower slopes. This corresponds to rising average product of
Ax until the point M and steadily declining average product thereafter.
It will be readily seen that M, E, correspond to the two points in the
isoquant map where the line GH was intersected by the two ridge lines.
The first stage, described in the laws of variable proportions, thus corre-
sponds to the portion of the curve from G to M°. In this region the average
output of Ay is increasing, and its marginal output is positive and greater
than the average output (as seen by comparing the slope of the output
curve at any point in this region, with the slope of the line joining this
point to the origin). In the diagram, since this portion of the output curve
was drawn concave from above, the marginal output also was increasing
during a portion of the range. The second stage described in the laws of
variable proportions corresponds to the portion of the output curve between
M° and E°. In this region the average and the marginal outputs are both
decreasing (but positive). The third stage corresponds to the region to the
right of E°; average output continues to fall and marginal output is nega-
tive. The points M°, and E°, have the special significance that for point
M° average output of Ay is at a maximum, while at point E° total output
is at a maximum (with marginal output of Ax zero).
Taking the more general approach, with the focus upon the ratio
between the inputs of the two factors rather than on the absolute input of
Alt we can easily see the application of the symmetry noticed earlier. The
situation in the first stage with respect to average and marginal output
of AJt with the quantity of Ax increasing, is completely mirrored in the third
section, with respect to average and marginal outputs of A2 considered for
a steadily decreasing input of Ax. In particular it is true that with constant
returns to scale, wherever the ratio of the input of either of the factors to
that of the other is so low that the average output of the first factor rises
with its increased input, then the situation is such that the other factor is
being so used that its marginal product is negative; output could be in-
creased by discarding some of this other factor. Moreover, at M°, where the
average product of A1 is at a maximum, the marginal output of A2 is zero
(that is, the total output yielded with any fixed quantity of Ax is maximized
when A2 is employed in the proportion denoted by the point M in Figure
8-11); and the converse of this proposition is true at the point E°.

The laws of variable proportions describe the pattern of technical condi-
tions that make up the background of the alternatives the producer-en-
trepreneur is able to choose from. In the market place, the precise

determination of these alternatives depends on the prices that quantities of
the factors can be bought at in the market.
Several generalizations can be made immediately. No entrepreneur
will under any circumstances employ a unit of a factor whose employment
causes output to decline. Thus, the laws of variable proportions tell us
immediately that there are opportunities open to the entrepreneur that
he will unquestionably reject. The entrepreneur will not employ factors
in a proportion that fits into either stage one or stage three of possible input
proportions. In either of these regions greater output could be obtained
simply by discontinuing the use of some of the factors. Thus, the very
important result is established that the only portion of the production sur`
face ever seriously under consideration is between the ridge lines. This
means that any group of factors employed in production will be in such a
proportion that (a) the per-unit output of each factor would be lower with
increased input, and (b) the marginal increment of product of any factor
would be lower with increased input. 13 (Increasing average or marginal
products can occur only where one of the factors has negative marginal
product; that is, in the regions outside the ridge lines.)
The goal of the entrepreneur is to produce his output at the lowest
possible cost. Of all the available alternative ways of producing a given
output, there will be one, or several, that require a smaller total outlay
than the others. Or, to put the matter the other way around, of all the
possible levels of output that it is possible to attain with a given cost out-
lay, one or several will be higher than the others. The entrepreneur will
seek to combine inputs in that proportion that will squeeze the most output
out of the cost outlay.
If either of the factors is a free good, it is very simple to determine
the optimum factor proportion. Additional units of this factor can be
obtained, for any given cost outlay, without forgoing the employment of
any of the other factor that it might be desirable to employ. The en-
trepreneur, thus, must simply buy as much of the priced factor as the given
cost outlay permits and then combine with it as much of the free factor as
will maximize output. That is, he must choose the proportion of the factors
at which the marginal output of the free good is zero (which is then also
the point where the average output attributable to the priced factor is at
a maximum). This point, of course, is at the boundary of the middle stage
(within which all entrepreneurs will, as we have seen, necessarily operate)
where the free good is employed relatively more freely.

13 One conceivable exception to these generalizations may result from a producer's
knowledge that the market price of his inputs and outputs depends very sensitively upon
his own production decisions. For the remainder of this chapter wTe ignore this possi-

Where, as is the usual case, both factors can be had only at a price, the
problem of determining the least-cost combination of factors for a given
output is very similar to the problem that the consumer faces in allocating
his income among several goods. In both cases the goal will be to ensure
that expenditure is distributed in such a way that were any sum of money
to be withdrawn at the margin from one good in favor of another, the
economizing individual would rank the sacrificed commodities higher on
his value scale than the additional commodities. In the case of the con-
sumer, the comparison involved the marginal utilities of the relevant com-
modities. For the producer the comparison can be made more objectively
in terms of the output given up, and the additional output gained. Thus
the least-cost factor combination, which the entrepreneur will consciously
seek to achieve, will be attained when the marginal increment of product
corresponding to the last "dollar's" worth of expenditure upon any one
factor is greater than the marginal increment of product corresponding to
a prospective additional expenditure of a dollar upon any other factor. If
this situation does not prevail, there is room to gain output, on balance, by
withdrawing money spent at the margin on one factor and expanding by
this amount the sum spent on other factors. This transfer will go on with
the consequence that the marginal increment of output corresponding to
the factor from which expenditure is being withdrawn will steadily rise
(because according to the law of variable proportions the relevant stage is
always that where the marginal output falls with greater inputs), while that
of the factors whose use is being expanded will fall, until the least-cost
combination is attained.
It is easy to see that with small-sized marginal units of factor (with
which the difference between the marginal increments of output corre-
sponding to two successively acquired units of factor can be ignored), this
least-cost combination condition can be stated as follows. The marginal
increments of product corresponding to units of any two factors must be
in the same proportion to one another as are their prices (MIPAl/MIP„2 =
price of ^j/price of A2). A given sum of money (S) being spent at the
margin on A2 (buying the quantity S/PAo, with P„9 the price of A2) makes a
difference to output responsible for S x MIPAo/PA(¬ output (approximately);
whereas the same amount of money spent on additional units of A1 could buy
V^¿i units > which could add (approximately) S X MIPAi/PAi in additional
output. But if, say, MIPAJM1PA2 > PAl/P„2 then MlPAJPAl > MIP„2/P„2
so that the transfer of expenditure at the margin from A2 to Ax would be
worthwhile. Thus, only equality between the two fractions describes the
situation where the least-cost combination has been attained.

The isoquant map provides, once again, a useful means for visualizing
the particular choice of input proportions that an entrepreneur will make
under given cost conditions. It is necessary to introduce once more a
graphic device that we have already met in the theory of consumer income
allocation”the constant expenditure curve. It will be recalled that if any
two goods, Ax and A2, can be obtained in any amount at constant prices per
unit (PAl and P¿2 respectively), then a line (BC in Figure 8-12) can be drawn

Figure 8-12

tracing out all the different packages of the two goods that a given sum of
money (say, S) can buy. For such a line, OB = S/P„2, and OC = S/PAl, so
that the slope BC with respect to the A1 axis is equal to P±JPA^` I*1 t n e
case of production, such a line passes through all the different factor com-
binations that can be bought for a given cost outlay and is given the name
isocost line.
When the isocost line is superimposed on an isoquant map, the points
where the isocost line is intersected by successive isoquants rank the differ-
ent factor combinations in order of their productive efficiency. The
particular choice of input proportions the entrepreneur seeks to achieve
corresponds to the point on an isocost line where it meets the highest of
these attainable isoquant levels.
In Figure 8-13 the isocost line BC (corresponding to a ratio of PAJPA» ”
OB/OC) is superimposed upon an isoquant map. It is evident that the
point P on the isocost corresponds to the particular factor combination that
yields highest output. It is at this point that the isocost is just tangent to an
isoquant. An any other point (for example, at T) the isocost can only
cut an isoquant; thus, there is a higher level of output that can be obtained
by giving up some of one input (for example, A2) and employing instead
additional units of the other (AA). At P, a transfer in either direction

would be disadvantageous because it could result only in lower output.
Any level of output higher than at P is simply out of reach with this outlay.
It will be observed that at the point of tangency, the slope of the
isoquant line is the same as that of the isocost; thus, this point fulfills the
(approximate) condition that the additional quantity of any one factor
necessary to offset the withdrawal from production of one unit of the

Figure 8-13

other factor be equal to the ratio of the price per unit of the second factor
to the price per unit of the first. This, of course, is simply the same
condition developed in the previous section, that the ratio between the
marginal increments of product corresponding to units of the two factors
be equal to the ratio of their prices.14
This graphic derivation of the least-cost condition provides an inter-
esting illustration of several of the principles developed in earlier sections
of this chapter. Thus the significance of the fact that the factors are not
perfect substitutes for one another is clearly brought out. If factors were
perfect substitutes so that the isoquants were straight lines, then, if the
slope of these isoquants were different from that of the isocost, there would
be no point of tangency at all. Substitution of one factor for another
would continue until only the one factor would be used. If the slope of

14 It may be observed at this point that much of the isoquant geometry developed in
this chapter has, in the literature, a counterpart in consumer theory. In the literature
the formal and diagrammatic analogy between consumer theory and production theory
has been carried forward very extensively. Corresponding to the isoquant map in produc-
tion theory, economists discuss the indißerence curve map in the theory of the consumer.
An indifference curve is a line drawn through all those different possible combinations
of two commodities between which a consumer feels indifferent. The approach to
consumer theory adopted in Chs. 4 and 5 made it unnecessary to resort to the use of
indifference curves (concerning which there are some rather serious theoretical problems).
The detailed discussion of isoquant maps in the present chapter, however, may be
applied to consumer theory without significant alteration if it is desired to employ the
indifference curve technique.

the isocost was that of the isoquants, then the isocost would coincide with
an isoquant throughout its length; thus, no particular proportion between
the two factors can be pronounced the most economic. (This, in fact,
would be the case where, as we saw, the two factors make up one homo-
geneous group. The equality in isocost and isoquant slopes simply means
that different prices are not being charged for economically identical units
of factors.)

Figure 8-14

Movement along an isoquant corresponds to an alteration of input
proportions. The fact that one such proportion is better than the others
is the corollary of the fact that the factors are not perfect substitutes for
each other. A change in the slope of the isocost (corresponding to a
relative cheapening of one of the factors, compared with the other) will
alter the point of tangency, either making a higher output possible for
the same outlay or bringing down the possible level of output. In any
event such a change will alter the optimum proportions of input in favor
of the factor that has become relatively cheaper.15
With a given relation between factor prices, it is possible to draw a
series of isocost lines, as BC, DE, FG . . . (in Figure 8-15). The respective

15 By an extension of the analysis of the least-cost combination, an insight can be
obtained into the notion of the demand curve for a factor of production. Such a curve,
for any one producer, reflects the different quantities of the factor that he asks to buy
at respectively different prices (all other things remaining unchanged). The lower the
price of a factor, the larger will be the quantity that a producer will generally wish to
buy. Our analysis explains part of the reason for this: the lower the price of a factor,
the more it pays to substitute it in place of other factors. The lower the price of a
factor, the greater becomes the marginal product derived from the last dollar spent on
it. Consequently the producer must (even if he were not to expand his output as the
result of the lower costs) switch expenditure at the margin from other resources to the
now cheaper resource, in order to achieve the (new) least-cost combination. (See also
Ch. 9, p. 200, ftnt. 10.)

points of tangency on these lines correspond to the different factor com-
binations that are optimum for successively higher levels of cost outlay.
Each such point makes the most of the relevant cost outlay; the entrepre-
neur has to select that level of outlay, which, taken in conjunction with
the price he can expect to get for his output, maximizes profits. The
path joining these points of tangency is appropriately named the expansion

0 C£ G I A%
Figure 8-15

We can refer graphically, finally, to the special case where one of the
factors is a free good, costing nothing to obtain. In this case, the isocost
line will be a straight line parallel to the axis of the free input. It will
show that a fixed quantity of the non-free input can be employed, with no
limit on the free input. The point of tangency with the isoquants will
be where the isoquants are vertical or horizontal; that is, on the ridge line.


At this point, as much of the free input is being used as can be employed
without diminishing possible output.

Chapter 8 commences the analysis of the activity of the individual
market participant in the role of producer. This analysis serves as the
foundation for the examination of the supply side of the market. The
economist sees the producer as making choices among alternatives of a
special kind. These alternatives involve the various productive uses that
the resources available to him might be put to. The rejected productive
uses constitute the economic costs of production of any adopted process
of production involving scarce resources. In society the efficiency of pro-
duction is advanced through specialization and division of labor. The
producer's alternatives are rigidly controlled by the market prices of the
resources he must purchase for a given production process.
Production is carried on with factors of production. A unit of factor
may possibly be related to a second unit of factor in a substitute relation-
ship, or possibly in a complementary relationship. A unit of factor may be
specific to the production of a certain product; it may be specialized for
this particular production; or, on the other hand, it may be versatile in
Analysis of production decisions is formalized by the use of several
mathematical and graphical concepts. Production possibilities are ex-
pressed in the production function, expressed graphically as the produc-
tion surface. Contour lines on this surface are isoquants. The slope of
the isoquants measure the substitutability between the cooperating factors.
Extreme cases are those where either no substitution at all is possible
(technically rigid proportions being required), or where the one factor may
be substituted completely for the second. Typical production processes
permit substitution between the complementary factors to a limited degree.
The isoquant geometry points up clearly the distinction between al-
terations in the proportions in which factors are combined, and alterations
in the scale in which factors (combined in a given proportion) are applied.
Alterations in scale yield alterations in output that may be characterized
by increasing returns to scale, decreasing returns to scale, or constant re-
turns to scale. Alterations in factor proportions yield alterations in out-
put that are governed by the laws of variable proportions. Detailed anal-
ysis of the various possible cases throws light on the alternative possible
ways of expressing these laws.
The economic implications of the laws of variable proportions include
the delimitation of the best input combination a producer will employ

under given technical and market conditions. The attainment of this
"least-cost combination" may be analyzed both logically and graphically.

Suggested Readings
Knight, F. H., Risk, Uncertainty and Profit, University of London (Reprint), Lon-
don, 1957, Ch. 4.
Carlson, S., A Study on the Pure Theory of Production, Kelley and Millman Inc.,
New York, 1956.
Stonier, A. W.”Hague, W. C , A Textbook of Economic Theory, Longmans Green,
London, 1953, Ch. 10.
Costs and Supply

A, of the operation
of the full market process must include, we have seen, the understanding
of the forces acting to supply the market with the various produced goods
and services. These forces determine the arrays of alternatives offered to
prospective consumers. But we have seen that these forces are themselves
conditioned by the circumstances under which entrepreneurs are able to
engage in production. In particular the entrepreneur operates in a situ-
ation where his choice of product, his choice of production method, and
his choice of volume of production must be made on the basis of the
market facts relating to the prices of both products and factors. In order
to produce any particular quantity of a particular product in a particular
way, the entrepreneur must pay definite costs of production. The quantity
of any one product that an entrepreneur will contribute to the market
supply, thus, will depend partly on the costs incurred for this output. The
quantity that the market as a whole will supply of any one product will
in turn depend partly on the costs of production that must be incurred
individually by entrepreneurs for the various possible levels of output.
In this chapter we carry further the analysis of the forces of supply.
Leaning heavily on the principles of production discussed in the previous
chapter, we examine especially the way costs of production of firms in a
particular industry are likely to change with output. The chapter carries
through the analysis to include the way the entrepreneur reacts to these
alternative production opportunities and the way is thus cleared to the
understanding of the forces of supply as they finally impinge on the market.
The focus of attention in this chapter is thus rather different from
that of the previous chapter. There we studied production, examining
the way output depended on the particular input combination employed.
Here we adopt a point of view corollary to that of the previous chapter;

here we are principally concerned with the way the costs of the firm depend
on the level of output. Unless otherwise specified, it may be assumed
throughout the chapter that for each output level, the least-cost combina-
tion problem has been solved. We turn first to a review of the ultimate
meaning of cost and its place in production theory.

The cost concept is bound up inseparably with the concept of human
action. Action consists in choosing between alternatives. The adoption
of any one specific alternative implicitly involves the rejection of other
alternatives; in particular it involves the rejection of the "second-best"
alternative”namely, that alternative that would have been adopted had
the alternative that was actually adopted been unavailable. It is this
rejected alternative that the economizing individual recognizes as the cost
of the adopted alternative simply because both opportunities cannot be
simultaneously adopted. A man may have to choose between the chance
of opening a certain kind of store on the one hand, and retaining the
friendship of a man engaged in the same line of business, on the other
hand. If he adopts the former alternative, then he recognizes that his
business has cost him his neighbor's friendship. Should he value the
friendship more highly, then the cultivation and preservation of this friend-
ship has cost him a possible lucrative business opening. Cost is made up
of the conscious sacrifice of an available opportunity. This is the most
general conception of the cost category.
For the isolated individual, the act of production involves a particular
aspect of cost. The employment of a unit of a non-specific resource for
the production of one particular product necessarily withholds it from
making any contribution to the production of other products. A decision
to make any particular use of a resource thus involves the sacrifice of other

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